Maximum principles and gradient Ricci solitons

It is shown that the Omori–Yau maximum principle holds true on complete gradient shrinking Ricci solitons both for the Laplacian and the f-Laplacian. As an application, curvature estimates and rigidity results for shrinking Ricci solitons are obtained. Furthermore, applications of maximum principles...

Full description

Saved in:
Bibliographic Details
Published inJournal of Differential Equations Vol. 251; no. 1; pp. 73 - 81
Main Authors Fernández-López, Manuel, García-Río, Eduardo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2011
Subjects
f-Laplacian
Gradient Ricci soliton
Omori–Yau maximum principle
Stochastically completeness
Stochastically completeness
f-Laplacian
Gradient Ricci soliton
53C25
Omori–Yau maximum principle
53C44
Online AccessGet full text

Cover

More Information
Summary:It is shown that the Omori–Yau maximum principle holds true on complete gradient shrinking Ricci solitons both for the Laplacian and the f-Laplacian. As an application, curvature estimates and rigidity results for shrinking Ricci solitons are obtained. Furthermore, applications of maximum principles are also given in the steady and expanding situations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2011.03.020